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Abdalla, I, Corda, J and Zhang, L (2016) Optimal control of a multilevel DC-link converter photovoltaic system for maximum power generation. Renewable Energy, 92. pp. 1-11. ISSN 0960-1481

https://doi.org/10.1016/j.renene.2016.01.062

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1

Optimal Control of a Multilevel DC-Link Converter Photovoltaic System for Maximum Power Generation

I Abdalla, J Corda, L Zhang

School of Electronic and Electrical Engineering, University of Leeds

Leeds LS2 9JT, United Kingdom E-mail: [email protected]

Abstract

This paper describes a new algorithm for optimal control of a PV system under partial shading. A

multilevel DC-link is the essential part of the proposed system and its control engages a voltage-hold

perturbation and observation (VH-P&O) method combined with a PWM algorithm with permutation

of PV sources. The algorithm enables achieving the maximum power generation for any number of

PV and converter modules. The main features of the control are: (i) a continual operation of all PV

sources, shaded and non-shaded, at their maximum power points, (ii) delivery of all extracted power

from PV sources to the load and (iii) generation of multilevel output voltage waveform with a low

total harmonic distortion.

Keywords: Multilevel Converters, MPPT, Partial Shading, Photovoltaic Panels

1 Introduction

PV power generators are commonly structured by connecting the PV modules in series to meet the

load voltage requirement. This configuration constrains that the same current flows through the chain.

However, the characteristics of the chained PV modules are not exactly identical even when they are

manufactured in the same batch. A more profound issue is the levels of illumination on individual PV

cells which may be different. Even if a single cell in the series chain is shaded, the current through the

whole chain would be reduced according to the shaded cell and consequently the overall power output

of the whole PV chain drops significantly. Furthermore the shaded cell or cells may be destroyed due

to the increased power dissipation on them resulting hot spots. A classical method to prevent high

power dissipation on shaded cells has been to connect bypass diodes across a set of chained cells

2

(normally 18). The drawback of such a method is that under uneven irradiance, when diode/s turn on

to allow the current flowing through, the power from individual cells is lost.

Various other methods have been developed to address the problem of partial shading. One of them

uses the Module-Integrated PV Converter (MIPC) scheme [1 - 4] which is formed from a series

connection of modules comprising a PV panel and a DC/DC converter. This enables the control of

each PV source output voltage for maximum power generation, while maintaining the same current

value at the converter output terminal. However the problem with this scheme is that the converter for

the shaded PV panel may only be able to maintain the current equal to that of the other modules when

the irradiance difference is moderate.

Departure from the maximum power point (MPP) may be unavoidable for a shaded source with a

larger light level discrepancy, and in this case the option may be to control the converter to bypass the

shaded source. Another approach relies on connecting the PV sources into a number of clusters of

nearly equal extracted power by using a switching matrix to reconfigure the clusters so that the PV

sources of equal shading, hence equal power generation, are connected in parallel. The method was

presented in [5, 6] and implemented experimentally in [7]. Although tests have shown that this

approach results in more power output than in the directly connected PV sources, the cluster which

generates the least power will be bypassed completely. The third scheme, named the ‘Generation

Control Circuit’ (GCC), uses a type of multilevel DC/DC converter with multiple DC/DC converters

connected in series, each powered by a PV source [8]. The individual converter may be a buck-boost

type and can be controlled to extract power from the PV sources and deliver it to the load directly.

This idea was implemented in [9] using a fly-back converter allocated to each PV source. The main

issue with this scheme is that the PV sources cannot be controlled completely independently.

Consequently, locating the MPP of one PV source does not mean that the other PV sources operate at

their MPPs.

This paper presents a novel optimal control scheme for a PV system using a converter topology called

the multilevel DC-link inverter. Similar to the MIPC above this system consists of multiple modules

3

connected in series, each module has a PV panel with a switch-diode pair at its output terminals. A

DC-AC bridge inverter is used at the output to convert the generated DC power into AC form [10].

The topology and control strategy enables the system to achieve the MPP tracking for all PV sources

in a system under any irradiation conditions. An initial investigation [11] has demonstrated the basic

converter topology and control concept. It has been shown that the scheme allows flexible control of

each PV source to make it operating at its respective MPP corresponding to its light level. In the

current paper a further improved control algorithm is presented which combines a voltage-hold

perturbation and observation (VH-P&O) method and the PWM algorithm with permutation of PV

sources for achieving the maximum power generation for any number of converter levels. The method

is presented by both simulation study and practical experimental test, and the results show a

significant enhancement of the PV system performance.

The paper is organised as follows. Section 2 describes the multilevel DC-link inverter topology. In

Section 3 the new control algorithm which combines the VH-P&O scheme and permutation PWM

strategy is presented in detail. Simulation study of the PV system and the control scheme, which is

performed using a STATE-SPACE AVERAGE model for the multilevel DC-link inverter, together with

the results obtained are discussed in Section 4. Finally, the experimental system and results obtained

by testing are presented in Section 5.

2 Structure of the PV System based on Multilevel DC-Link Converter

Fig. 1 shows the configuration of a PV system comprising three PV units acting in conjunction with a

multilevel DC-link converter. Each PV unit consists of a single PV source, a capacitor and a switch

with a complimentary diode. The units are connected in series and any of them can be switched in or

out of the chain by turning on or off its switch. When a unit is switched off, it is being bypassed by a

diode. The three switches (SW1, SW2, SW3) operate at a high frequency and are controlled by the

direct PWM method [12] to form a three-level positive DC voltage. The H–bridge inverter at the

output serves to convert the multilevel DC voltage waveform to alternative positive and negative

4

output voltage half-cycles of the required output frequency (e.g. 50Hz). The generation of multiple

voltage levels, combined with proper control, enables forming the approximate sinewave output.

PV1

PV2

CPV1

CPV2

Vout

Iout

S1 S3

S2 S4

+

VPV1

-

+

VPV2

-

IPV1

IPV2

P&O

MPPT2

SW1

SW2

Vlink

sin(wrt)

SW switches operate at high

PWM frequency (kHz) S switches operate at low

frequency (50Hz)

Lo

ad

Vref1

Vref2

×

×

PV3

CPV3+

VPV3

-

IPV3

SW3

×

P&O

MPPT3

P&O

MPPT1

Vref3

PV permutation

algorithm

t

vlink

vout

Control

Unit

t

Fig. 1: PV system with multilevel DC- link converter

3 Optimal Control Scheme based on Permutation of PV Sources

The optimal control scheme should maximise the power transferred from PV sources to the AC load

or grid in different light conditions, and generate a nearly sinusoidal voltage with minimum harmonic

distortion and DC offset. Ideally, it should also ensure equal switching utilisation and hence the

losses. The solution presented in this paper comprises two parts: (i) Voltage-Hold Perturb & Observe

(VH P&O) method for generation of the MPP reference voltage and (ii ) PWM algorithm with

permutation of PV sources for switching control.

5

3.1 The Voltage-Hold P&O Method for Reference Voltage Generation

A classical strategy for the PV maximum power point tracking is the perturbation and observation

(P&O) method, which has been widely studied and used in the PV MPPT controllers (e.g. [13-17]).

The two problems linked with this simple search method are that the terminal voltage may oscillate

around a MPP, and the system may lose the MPP during rapid irradiance changes. Some

improvements have been proposed for reducing the number of oscillations around MPP (e.g. [18,

19]), but a slow speed of the response may result in an incorrect MPPT if the changes of irradiance

are rapid.

The voltage-hold (VH) P&O method proposed here overcomes the above limitation in terms of

oscillations around MPPs, which cause noise and slow down the search process, and also it can cope

with rapid irradiance changes. For solving the problem of oscillating around a MPP, the algorithm

uses variable searching step size. As soon as the irradiation change stops, the tracking step size is

gradually decreased towards zero when reaching close to the MPP. When an irradiation change

occurs, the tracking step size will be reset to the initial value to maintain the fast tracking. At a rapid

irradiance change, which can be detected by measuring the light level and the number of changes

within a fixed time interval, the algorithm stops the searching process and sets the reference voltage to

the measured PV capacitor voltage which is essential tracking quantity. Subsequently the algorithm

resumes the perturbation process for searching the MPP voltage along the I-V characteristic

corresponding to the new light level.

The VH P&O method is applied in sequence to each PV unit at each sampling instant, to track

individually their respective reference voltages. This may lead to different voltage values depending

on the weather conditions and PV panel characteristics. For generating AC reference voltages these

values are multiplied by a unity sinusoidal signal sin のt (の = 2ヾ × 50). (For example, in the system

with three PV units, the reference voltages vref1(t), vref2(t) and vref3(t) are generated as shown in

Fig.1.)

6

3.2 PWM Algorithm with Permutation of PV Sources

The next step should naturally be generation of PWM signals for the switches of individual PV units.

For maximum power extraction, the terminal voltage of each PV unit should be as close as possible to

its individual reference voltage established by the VH P&O process. This also implies that with

multiple PV units in a chain, the PWM reference signal for the whole system should be the sum of all

individual reference voltages, i.e. vref1(t)+ vref2(t),…+ vref(n)(t). To meet these conditions and the criteria

of equal switch utilisation and low waveform distortion, a novel PWM algorithm based on

permutation of PV sources has been developed. The algorithm consists of three stages, which are

performed within each PWM switching period Ts: the direct PWM [12], the sequential permutation of

PV sources, and the AC output voltage generation.

In Stage 1, the direct PWM determines the output voltage levels and switch-on time intervals as

follows. The reference voltages vref(j)(t) (j = 1,…n), obtained from VH P&O process, are normalised as

nV

tvv

jj /

)(

L

)ref()ref( (1)

where the standard voltage level VL equals VMPP for a single source (panel) at the standard irradiance

of 1000 W/m2 and temperature 25ºC, and n is the total number of PV sources. (This makes normalised

voltages n×vref(j)/VL, i.e. they are normalized for the full system comprising n sources.)

The integer part of each normalized reference voltage is defined as the offset voltage, i.e.

][int )ref()offset( jj vv (2)

If voffset(j) > 1, the switch of the corresponding PV source should be in 'on' state during time interval

)( )offset()ref(s)on( jjj vvTt (3)

On the other hand if voffset(j) = 0, the switch of the corresponding PV source should be in 'off' state to

allow the diode to bypass this source. Stage 1 generates all n values of voffset(j) and ton(j).

In Stage 2, the sequential permutation algorithm is implemented to determine the switching states of

all PV units for building up the output voltage of the system. All PV sources are sequentially

permutated through consecutive PWM switching cycles according to the cyclic counter C as

7

illustrated in Fig.2. The PV source which sequentially comes in turn at the highest voltage level is the

only one which is controlled at a particular switching period (Ts), while other sources are used to build

up the appropriate voltage level. The benefits of such a process are: (i) all PV sources of the system

are equally engaged and the switching losses of transistors associated with each PV source are

balanced, (ii) the achievement of symmetrical positive and negative half-cycles of the AC output

waveform under partial shading and (iii) the reduction of the voltage ripple on capacitors of PV units.

t

Vout

Voh

Ts

PV

1

PV

2

PV

1P

V3

PV

2P

V1

PV

2P

V3

+P

V1

PV

3P

V1

+P

V2

PV

1P

V2

+P

V3

VPV

2VPV

3VPV

Vol

ton toff

C=1 C=2 C=3 C=1 C=2 C=3 C=1

Fig. 2: Permutation of PV sources through consecutive PWM switching cycles

Unlike the basic algorithm [11], the improved algorithm does not represent the PV source at the

output if its offset voltage is zero, except in the case when all offset voltages are zero. The reason for

introducing this exception is to initiate the control and it is also required in the case of low PWM

reference signals.

In Stage 3 the terminal H-bridge converter is used to change the multilevel DC voltage waveform to a

single-phase AC waveform of low frequency (e.g. 50 Hz) by tracking the sinusoidal reference signal.

Table 1 presents the switching states and output voltage generation for the system with three PV

sources (n = 3). According to formulae (1) - (2), the offset voltages voffset(j) (j = 1,2,3) can be either 0, 1

or 2. Hence there are 27 combinations in total and 27 output voltage patterns, which makes the

presentation quite cumbersome. For clarification, a graphical illustration of the process for generating

the output waveform in the basic system with two PV sources is given in the Appendix.

8

Table 1: Switching states and output voltage generation for the system with three PV sources

C voffset1 voffset2 voffset3 Vol Voh ton

1 0 0 0 0 VPV1 ton1

0 0 1 0 0

0 0 2 VPV3 VPV3

0 1 0 VPV2 VPV2

0 1 1 VPV2 VPV2

0 1 2 VPV2+VPV3 VPV2+VPV3

0 2 0 VPV2 VPV2



1 0 0 0 VPV1

1 0 1 0 VPV1

1 0 2 VPV3 VPV1+ VPV3



1 1 2 VPV2+VPV3 VPV1+ VPV2+ VPV3




2 0 0 0 VPV1









2 0 0 0 0 VPV2 ton2

0 0 1 VPV3 VPV3

0 0 2 VPV3 VPV3

0 1 0 0 VPV2

0 1 1 VPV3 VPV2+VPV3


0 2 0 0 VPV2



1 0 0 0 0

1 0 1 VPV3 VPV3


1 1 0 0 VPV2






2 0 0 VPV1 VPV1

2 0 1 VPV1+VPV3 VPV1+ VPV3







2 2 2 VPV1+VPV3 VPV1+ VPV2+ VPV3 c

Continued …

C voffset1 voffset2 voffset3 Vol Voh ton

3 0 0 0 0 VPV3 ton3

0 0 1 0 VPV3

0 0 2 0 VPV3

0 1 0 0 0

0 1 1 0 VPV3


0 2 0 VPV2 VPV2



1 0 0 VPV1 VPV1



1 1 0 VPV1 VPV1






2 0 0 VPV1 VPV1









9

4 Simulation of the PV System Performance

The multilevel DC-link converter is simulated using a state-space average (SSA) model having the

general form given by [20]:

)pv(

2pv

1pv

)pv(

2pv

1pv

)pv(

2pv

1pv

)pv(

2

)pv(

2

)pv(

1

2pv

2

2pv

22

2

12

1pv

1

1pv

21

1pv

21

)pv(

2pv

1pv

100000

00000

0000

000

001

0

001

1

d

d

d

dd

d

n

n

n

n

n

n

n

n

n

n

pv

n

ni

i

i

C

C

C

v

v

v

C

D

C

DD

C

DD

C

DD

C

D

C

DD

C

DD

C

DD

C

D

R

t

v

t

vt

v

(4)

)pv(

2pv

1pv

21out )12(

n

n

v

v

v

DDDDv

(5)

where, the input vector elements are the currents ipv1, ipv2,…ipv(n) of PV sources; the terminal voltages

vpv1, vpv2,…vpv(n) form the state vector; Cpv1, Cpv2,…Cpv(n) are the corresponding terminal capacitances;

Dl, D2, … Dn are the state variables for switches SW1, SW2… SW(n); R is the load resistance; D is the

state variable of the single-phase output H-bridge inverter (D = 1 when S1&S4 are switched on, and D

= 0 when S2&S3 are switched on).

Elements of the input vector [ipv1, ipv2,…ipv(n)] are found from the MPPs of the I-V characteristics

which are generated using Bishop’s model for the PV source [21]. The I-V characteristics for different

irradiance levels are shown in Fig.3 with indicated MPPs. Table 2 lists the system parameters used in

the model.

10

Voltage (V) 0

5

10

15

20

0 5 10 15 20 25 30 35 40 45 50 55 60 64

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Ipv(

A)

2

21000 W/m

2750 W/m

2500 W/m

250 W/m

5 A, 50 V250 W

3.74 A, 48.62 V181.9 W

2.48 A, 46.66 V115.9 W

1.23 A, 43.33 V53.38 W

Cu

rre

nt (A

)

Fig. 3: I-V characteristics of the PV source for different irradiance levels

(MPP is indicated on each characteristic.)

Table 2: PV system parameters used in simulations

The waveforms were simulated for the PV systems with n = 2, 3, 4 and 5 sources generating

respectively five, seven, nine and eleven-level AC output voltages. The Fast Fourier Transformation

(FFT) is applied to the output waveform to evaluate the fundamental harmonic and the total

harmonics distortion (THD).

Symbol Parameter Value

PMPP Maximum power of PV source 250 W

Cpv PV source terminal capacitor 5500 ȝF

R Load resistance

8.5 Ω (5&7-level)

18.5 Ω (9-level)

23 Ω (11-level)

ev P&O tracking step size 0.5 V

Mf Frequency modulation index 100 (5-level)

300 (7,9&11-level)

f AC output frequency 50 Hz

11

Fig. 4a shows five-level output voltage waveforms produced by the system with two sources PV1 and

PV2 exposed to irradiances of 500 W/m2 and 1000 W/m2 respectively. The improved algorithm gives

better voltage waveforms (shown on the right) compared with its predecessor. The THD of 43.5% and

the 50-Hz fundamental peak voltage V1(p) = 76.8 V were achieved with the improved algorithm,

compared to the THD of 58.65% and V1(p) = 70.7 V achieved with the predecessor. Similar comparison

was made for the seven-level converter with three PV sources at irradiances of 1000, 500 and 1000

W/m2 applied to PV1, PV2 and PV3 respectively. The output voltage waveforms are shown in Fig.

4b. The improved algorithm generates substantially better waveform with THD = 35.72% and V1(p) =

108.64 V, compared to the THD = 57.41% and V1(p) = 95.81 V achieved with the predecessor.

Fig. 4: Output voltage waveforms simulated by the predecessor and the improved algorithm.

(a) five-level AC waveforms with sources PV1 and PV2 at irradiances 500 and 1000 W/m2;

(b) seven-level AC waveforms with sources PV1, PV2 and PV3 at irradiances 1000, 500 and

1000 W/m2 respectively.

Predecessor algorithm Improved permutation algorithm

1.8 1.805 1.81 1.815 1.82-100-75-50-25

0255075

100

Vout

(V)

1.35 1.355 1.36 1.365 1.37-100-75-50-25

0255075

100THD=58.65%,V1(p)=70.72V

THD=43.52%,V1(p)=76.81V

Time (s) Time (s)

(a)

Predecessor algorithm Improved permutation algorithm

3.27 3.275 3.28 3.285 3.29-150

-100

-50

0

50

100

150

Vou

t (V

)

4.99 4.995 5 5.005 5.01-150

-100

-50

0

50

100

150THD=57.41%,V1(p)=95.81V

THD=35.72%,V1(p)=108.64V

Time (s) Time (s)

(b)

12

Fig. 5 illustrates output voltage waveforms and power extracted from the system with four PV sources

using 9-level converter for two cases – (a) none of the sources are shaded and (b) one source is

shaded. The power levels extracted from individual sources and the load power are shown by line

graphs on the right-hand side. Referring to Fig. 5a, when all four PV sources are exposed to equal

irradiance of 1000 W/m2, the THD is 18.4%, the 50-Hz fundamental peak voltage V1(p) = 194 V and

the power extracted from each panel is 250 W giving 1000 W to the load. Referring to Fig. 5b, when

one source is shaded, i.e. exposed to the halved irradiance (500 W/m2), the predicted THD is 21.67%,

V1(p) = 176 V and the total power delivered to the load is 865 W conforming that it is very close to

the sum of maximum power values found from I-V characteristics (3x250+116 W).

Fig. 5: Simulated output voltage waveforms and the extracted power achieved by the improved

algorithm for 9-level converter with four PV sources.

(a) all at the same irradiance of 1000W/m2;

(b) at irradiances of 1000 W/m2 for PV1, PV2, PV3 and 500W/m2 for PV4.

2.81 2.815 2.82 2.825 2.83

-200

-100

0

100

200

Vou

t (V

)

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 30

100200300400500600700800900

1,000

Pow

er (W

)

PV1,2,3,4

Load pow erTHD=18.40%

V1(p)=194.16V

Time (s) Time (s)

(a)

2.55 2.555 2.56 2.565 2.57

-200

-100

0

100

200

Vou

t (V

)

2 2.2 2.4 2.6 2.8 30

100200300400500600700800900

1,000

Pow

er (w

)

PV1,2,3

Load pow er

PV4

THD=21.67%V1(p)=176.26V

Time (s) Time (s)

(b)

13

Fig. 6 illustrates another example, which relates to the system with five PV sources and using 11-level

converter. Referring to Fig. 6a, when all sources are exposed to equal irradiance of 1000 W/m2, the

values of THD and the 50-Hz fundamental peak voltage V1(p) are respectively 14.95% and 241 V and

both are improved compared to the values achieved by 9-level converter (18.4% and 194 V). Fig. 6b

relates to the state when PV sources are exposed to different irradiances (250, 500, 750, 750 and 1000

W/m2). The predicted THD is now 19.48%, and the total power delivered to the load is 790W which

is very close to the sum of maximum power values of five PV sources found from I-V characteristics

(53W, 116 W, 2x182 W and 250 W).

Fig. 6: Simulated output voltage waveforms and the extracted power achieved by the improved

algorithm for 11-level converter with five PV sources.

(a) all at the same irradiance of 1000W/m2;

(b) at irradiances of 250, 500, 750, 750 and 1000 W/m2.

Fig. 7 illustrates the dynamic performance in terms of extracted power from each PV source and the

total power delivered to the load from 7-level converter for a sequence of irradiance variations.

Initially the full irradiance of 1000 W/m2 is applied to all three PV sources and 250 W is extracted

3.71 3.715 3.72 3.725 3.73

-200

-100

0

100

200

Vou

t (V

)

2.5 2.6 2.7 2.8 2.9 30

100200300400500600700800900

1,0001,1001,2001,300

Pow

er (W

)

PV1,2,3,4,5

Load power

THD=14.95%V1(p)=240.67V

Time (s) Time (s)

(a)

3.85 3.855 3.86 3.865 3.87

-200

-100

0

100

200

Vou

t (V

)

2.5 2.6 2.7 2.8 2.9 30

100200300400500600700800900

1,0001,1001,2001,300

Pow

er

(W)

PV3,4

Load power

THD=19.48%V1(p)=209.12V

PV5PV2PV1

Time (s) Time (s)

(b)

14

from each source delivering a total of 750 W to the load. In the time between 2 and 5 seconds, the

irradiance to PV3 source is halved (500 W/m2), while PV1 and PV2 are still at full irradiance. The

extracted power from PV3 is now reduced to 116 W, which matches the MPP on the I-V

characteristic at irradiance of 500 W/m2 in Fig.3. The power levels from PV1 and PV2 are not

affected by the shading of PV3, so the total delivered power is 616 W. During the time interval

between 5 and 8 seconds, both PV2 and PV3 are shaded at the halved irradiance (500 W/m2) while

PV1 is under full irradiance, and the delivered power is 482 W. Between 8 and 11 seconds, all three

PV sources are shaded to the halved irradiance (500W/m2), and the power delivered to the load is

reduced to 348 W. After 11 seconds all three PV sources are again exposed to the full irradiance and

are recovered to their MPPs of 250 W delivering the power of 750 W to the load.

Fig. 7. Power responses of the system with seven-level DC-link converter during irradiance changes.

(a) irradiance variations in time;

(b)-(d) extracted power from individual sources PV1, PV2 and PV3;

(e) total power delivered to the load.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 1010.51111.51270

100130160190220250

PV

1 P

ower

(W

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 1010.51111.51270

100130160190220250

PV

2 P

ower

(W

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 1010.51111.512100125150175200225250

PV

3 P

ower

(W

)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 1010.51111.512250350450550650750

Load

pow

er (

W)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 1010.51111.512450550650750850950

1050

Irra

dian

ce (

W/m

)

Time (s)

PV3 PV2 PV1

2

15

5 Experimental Results

Laboratory experiments were performed on a system having three identical small serially connected

PV modules (sources) with an in-house built 7-level converter. Each module was exposed to a

separate artificial sunlight with adjustable irradiance emulated by three halogen bulbs each of which

was supplied from a different phase of a 3-phase variac connected to the 3-phase 50-Hz mains supply.

This arrangement provides a fairly uniform irradiance to each module.

The parameters of the experimental system are listed in Table 3. The measured I-V characteristic of

the PV module are shown in Fig. 8 under different irradiance levels at room and surface temperatures

of 20°C and 38°C respectively.

Table 3: Experimental system parameters

Though the power ratings of the PV panels are lower than those used in the simulation study, this is

considered adequate for verifying the principle of the proposed control scheme for the following

reasons: (i) With the artificial sun light simulator set up in the available laboratory, the measured I-V

characteristics of small PV panels corresponding to various light and temperature levels follow

closely the characteristics given in the data sheets. However, panels with higher power rating (over

100 W) give significantly lower output power compared to what they should generate based on the

data sheet; (ii) For validating the proposed control scheme the difference in power rating is not

considered an issue, because the controller can be scaled up for higher power system without causing

dynamic stability problems.

Symbol Quantity Value

PMPP PV source maximum power 10 W

Cpv PV source terminal capacitor 2200 ȝF

R Load resistance 30 Ω

ev P&O tracking step size 0.2 V

Mf Frequency modulation index 100

f Output frequency 50 Hz

16

Fig. 8. Measured I-V characteristic of a 10W PV module at different irradiances

The improved control algorithm has been applied to the experimental system. The control is

implemented via a digital processing unit eZdspTM F28335 in real-time [22], and the Matlab-Simulink

real time data exchange (RTDX) is employed to display the extracted power and to modify the system

parameters via a graphical user interface (GUI). Details of this are presented in [21].

The extracted power from each PV module can be monitored on the bar chart of the GUI window in

real-time mode as illustrated in Fig. 9 which shows two examples with different shading conditions.

The graphs demonstrate that the developed system ensures that shaded PV module/s do not affect the

operation of non-shaded module/s which continue to generate their maximum power.

Fig. 9: GUI window showing the extracted power from each PV module at different irradiances

1000 W/m2

725 W/m2

580 W/m2

435 W/m2

290 W/m2

145 W/m2

70 W/m2

0

0.1

0.2

0.3

0.4

0.5

0.6

Voltage (V) 0

5

10

15

20

0.7

Cur

rent

(A)

17

Table 4 summarizes the THD and the 50Hz fundamental amplitude of the load voltage waveforms

which are shown in Fig. 10 for both the previous and improved PV permutation algorithms as a

function of the PV extracted power. It is apparent that at the same conditions of partial shading, the

improved PV permutation algorithm has resulted in a lower output harmonic distortion and larger

amplitude of the fundamental harmonic (50 Hz), compared to the precursor algorithm.

Fig.10: Output voltage and current waveforms of 7-level converter: measured under control by

precursor algorithm (column 1); measured and simulated under control by improved

algorithm (columns 2 and 3). Irradiances applied to sources PV1, PV2 and PV3 in W/m2,

top to bottom row: (1000, 500, 1000); (1000, 1000, 150); (1000, 750, 250); (500, 1000, 250).

-4

-3

-2

-1

0

1

2

3

4

-4

-3

-2

-1

0

1

2

3

4

-4

-3

-2

-1

0

1

2

3

4

-4

-3

-2

-1

0

1

2

3

4

THD=40.26%, V1(p)=35.16V

THD=34.80%, V1(p)=33.26V THD=55.21%, V1(p)=30.83V

THD=40.50%, V1(p)=31.37V THD=64.92%, V1(p)=29.91V

THD=38.46%, V1(p)=29.07V THD=61.22%, V1(p)=27.95V THD=43.65%, V1(p)=29.37V

THD=42.38%, V1(p)=31.80V

Vol

tage

(V)

60 40 20 0 -20 -40 -60

Cur

rent

(A) 2

0 -2

Vol

tage

(V)

60 40 20 0 -20 -40 -60

Cur

rent

(A) 2

0 -2

10ms

Vol

tage

(V)

60 40 20 0 -20 -40 -60

Cur

rent

(A) 2

0 -2

Vol

tage

(V)

60 40 20 0 -20 -40 -60

Cur

rent

(A) 2

0 -2

THD=36.00%, V1(p)=36.33V THD=34.05%, V1(p)=36.23V

THD=33.68%, V1(p)=34.18V

(a)

(b)

(c)

(d)

iout

vout

iout

vout

iout

vout

Time (10 ms / div) Time (10 ms / div) Time (10 ms / div)

18

Table 5 lists the numerical values obtained by measurements and simulation of the power delivered to

the load when the improved control algorithm is applied. The small discrepancies between measured

and simulated results are principally caused by the inverter losses which were not accounted for in

simulations.

Table 4: Summary of measured and simulated results at various shading levels

Table 5: Measured and simulated values of power delivered to the load at various shading levels

6 Conclusions

The main features of the newly developed control scheme, which uses the VH P&O method and

improved PV source PWM permutation algorithm, are: (i) the upholding of operation of all PV

sources (shaded or not shaded) at their MPPs, (ii) the delivery of all extracted power from PV sources

to the load and (iii) the generation of improved multilevel voltage waveforms with low THD.

Extracted power (W) Precursor algorithm

Measured results Improved algorithm

Measured results Improved algorithm Simulated Results

PV1 PV2 PV3 THD (%) V1(P) (V) THD (%) V1(P) (V) THD

(%) V1(P) (V)

10 5 10 40.26 35.16 36.00 36.33 34.05 36.23

10 10 1.5 55.21 30.83 34.80 33.26 33.68 34.18

10 7.5 2.5 64.92 29.91 40.50 31.37 42.38 31.80

5 10 2.5 61.22 27.95 38.46 29.07 43.65 29.37

Extracted power (W) Measured

Load Power (W)

Simulated

Load Power (W) PV1 PV2 PV3

10 10 10 28.89 29.96

10 5 10 23.81 24.96

10 10 1.5 21.01 21.44

10 7.5 2.5 19.34 19.98

5 10 2.5 17.20 17.49

19

The proposed system was simulated using Matlab–Simulink for multilevel DC link converters with

five, seven, nine and eleven-level AC output voltages. Static and dynamic irradiance levels were

applied to test the system behaviour with respect to the MPP tracking and the quality of the output

waveforms. The comparison between the previous and the improved algorithm have shown that the

latter generates a lower distortion of the waveform and higher amplitude of the fundamental (50-Hz)

harmonic of the output voltage. Experimental tests on a small-scale system, which uses three PV

sources and seven-level DC-link converter, have validated the advantages of the new scheme.

The time varying irradiance levels were applied to test dynamic behaviour of the system in terms of

the MPP tracking. The algorithm enables the recovery of each shaded PV source to its MPP without

affecting other PV sources connected in the chain.

Appendix

When C = 1:

If voffset1 is either 0 or 1 and voffset2 = 0, then:

SW1 is ‘on’ during interval ton1 and ‘off’ otherwise;

SW2 is ‘off’ during entire period Ts.

If voffset1 = 0 and voffset2 = 1, then:

SW1 is ‘off’ and SW2 is ‘on’ during entire period Ts.


SW1 is ‘on’ during interval ton1 and ‘off’ otherwise;

SW2 is ‘on’ during entire period Ts.

When C = 2:

If voffset2 is either 0 or 1 and voffset1 = 0, then:

SW1 is ‘off’ during entire period Ts;

SW2 is ‘on’ during interval ton2 and ‘off’ otherwise.

If voffset2 is 0 and voffset1 = 1, then:

SW2 is ‘off’ and SW1 is ‘on’ during entire period Ts.


SW1 is ‘on’ during entire period Ts;

SW2 is ‘on’ during interval ton2 and ‘off’ otherwise.

20

In Fig. A1, vref1 and vref2 are two reference voltages of the five-level converter. These signals are

sampled at periods Ts yielding Mf samples for each reference signal over the time period Tr = 1/fr. (fr

denotes the required output frequency, e.g. 50 Hz.) At each period Ts, the sampled values are applied

to the Eqs. (1) - (3) for generating the required control signals.

t

vref2

t

vout

TS

VL

t

t

t

t

SW1

SW2

S1S4

S2S3

t

vref1

VL

1C 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1

VP

V2

VP

V2

VP

V1

VP

V2

VP

V1

VP

V2

VP

V1

VP

V2

VP

V1

VP

V2

VP

V1

VP

V1

VP

V1

VP

V2 +

VP

V1

VP

V1 +

VP

V2

TS Tr /2

Fig. A1: Graphical illustration of the process for generating the output waveform in the basic

system with two PV sources

21

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22

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